In a small bowl, combine mayonnaise, ketchup, sweet pickle relish, and Worcestershire sauce to make the secret sauce. Set aside.

In a large skillet, melt 1 tablespoon of butter over medium heat. Add the sliced onions and cook, stirring occasionally, until caramelized, about 15–20 minutes. Remove and set aside.

Divide ground beef into 4 equal portions and shape into thin patties. Season both sides with salt and pepper.

Cook patties in the same skillet over medium-high heat until cooked through, about 3–4 minutes per side. Remove and set aside.

Butter one side of each slice of rye bread. Place 4 slices, butter-side down, on a skillet or griddle over medium heat.

Top each with a slice of Swiss cheese, a cooked patty, caramelized onions, a slice of cheddar cheese, and another slice of bread, butter-side up.

Cook until the bread is golden brown and the cheese has melted, about 2–3 minutes per side.

Remove from the skillet and let rest for 1 minute. Slice in half and serve immediately with the secret sauce on the side or drizzled over the top.